In the classical solutions framework, there are mainly two approaches: one is based on the spectral analysis of semigroup and another is the nonlinear energy method. For the former approach, Bardos and Ukai [1]} took the first step to obtain the uniform in \(\varepsilon \in (0,1)\)  (the Knusden number) global existence of classical solution to scaled Boltzmann equation for hard cutoff potential. As a result, they also established the incompressible Navier-Stokes limit from Boltzmann equation. More contributions refer to the literatures [2]}, [3]}, [4]}, [5]}. For the nonlinear energy method developed by Guo [6]}, [7]}, we focus on its application to the compressible Euler limits although there are many results (c.f. [8]}, [9]}, [10]}) of incompressible fluid limits. As an improvement of Caflisch's work [11]} where the truncated Hilbert expansion with a remainder was used, Guo-Jang-Jiang [12]} made the first step to prove the compressible Euler limit and acoustic limit in optimal scaling from Boltzmann equation by employing the nonlinear energy method. This method relies on our knowledge of the local well-posedness of compressible Euler equation in advance.
